Jorge Laval, Ph.D.
Associate Professor, Civil Engineering
Georgia Institute of Technology
This presentation focuses on a formulation of the reactive dynamic user equilibrium problem in continuum form using a network-level Macroscopic Fundamental Diagram (MFD). Compared to existing continuum models for cities -- all based in Hughes' pedestrian model in 2002 -- the proposed formulation (i) is consistent with reservoir-type models of the MFD literature, shedding some light into the connection between these two modeling approaches,(ii) can have origins and destinations continuously distributed on the region, and (iii) can incorporate multi-commodity flows without additional numerical error. The proposed multi-reservoir numerical solution method treats the multi-commodity component of the model in Lagrangian coordinates, which is the natural representation to propagate origin-destination information (and any vehicle-specific characteristic) through the traffic stream. Fluxes between reservoir boundaries are computed in the Eulerian representation, and are used to calculate the speed of vehicles crossing the boundary. Simple examples are included that show the convergence of the model and its agreements with the available analytical solutions. We find that (i) when origins and destinations are uniformly distributed in a region, the distribution of the travel times is given by a one parameter scaling of the free-flow travel time distribution, (ii) the magnitude of the detours from the optimal free-flow route due to congestion increase linearly with the inflow and decreases with the square of the speed, and (iii) the total delay of vehicles in the network converges to the analytical approximation when the size of reservoirs tends to zero.
Jorge Laval is an Associate Professor at the School of Civil and Environmental Engineering since 2006. After obtaining his B.S. in Civil and Industrial Engineering from Universidad Catolica de Chile in 1995, Dr. Laval worked as a transportation engineer for 5 years at the Chilean Ministry of Public Works in Santiago, Chile. He received his Ph.D. in Civil Engineering from the University of California, Berkeley in 2004. Prior to joining Georgia Tech, Dr. Laval held two consecutive one-year postdoctoral positions at the Institute of Transportation Studies at UC Berkeley, and at the French National Institute for Safety and Transportation Research (INRETS/ENTPE). Professor Laval's main research thrust is in the area of traffic flow theory, modeling and simulation, focusing in understanding congestion in urban networks and how to manage it. He has made important contributions towards understanding the capacity of freeways, the connection between driver behavior and stop-and-go waves, freeway ramp-metering strategies, dynamic traffic assignment and congestion pricing.